Combined Hypothesis Testing on Graphs with Applications to Gene Set Enrichment Analysis

Area of Science:

• Statistics
• Bioinformatics
• Computational Biology

Background:

• Gene set enrichment analysis (GSEA) motivates the need for advanced statistical methods.
• Traditional methods may not fully utilize complex data structures like graphs.
• Testing multivariate means requires robust approaches that account for relationships within data.

Purpose of the Study:

• To develop a general framework for combined hypothesis testing on graphs.
• To propose a novel testing procedure that effectively uses graph structural information.
• To establish the optimality and performance bounds of the new testing method.

Main Methods:

• A general framework for graph-based hypothesis testing is introduced.
• A new optimal testing procedure is developed within this framework.
• Performance bounds are derived for various graph types, supported by numerical experiments.

Main Results:

• The proposed test is shown to be optimal for detecting departures from the collective null hypothesis across most graphs.
• General performance bounds are provided for specific graph structures.
• Numerical experiments validate the effectiveness and advantages of the new approach.

Conclusions:

• The novel graph-based framework offers an effective way to test multivariate means.
• The proposed optimal testing procedure enhances statistical power by utilizing graph information.
• This approach has significant implications for fields like bioinformatics and systems biology.